JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 July 2022, Shift 1, Maths Q4

Question 4 of 90 in this shift, Maths question 4 of 30, Section A.

The number of

\theta\in(0,4\pi)

for which the system of linear equations

3(\sin 3\theta)x-y+z=2

3(\cos 2\theta)x+4y+3z=3

6x+7y+7z=9

has no solution, is :

(1) $6$
(2) $7$ Official answer
(3) $8$
(4) $9$

Official answer

Option 2

NTA final key (2022 Session 2).

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Trigonometric Coefficients and Solution Counting

Same topic in other shifts

All Cramer's Rule questions

2 Apr 2026, Shift 1 · Q3Let $\alpha, \beta \in \mathbf{R}$ be such that the system of linear equations $x+2y+z=5$ $2x+y+\alpha z=5$ $8x+4y+\beta z=18$ has no…MediumSingle correct
2 Apr 2026, Shift 2 · Q3If the system of equations $x + 5y + 6z = 4,$ $2x + 3y + 4z = 7,$ $x + 6y + az = b$ has infinitely many solutions, then the point $(a, b)$ …MediumSingle correct
4 Apr 2026, Shift 2 · Q3If the system of equations: $x+y+z=5$ $x+2y+3z=9$ $x+3y+\lambda z=\mu$ has infinitely many solutions, then the value of $\lambda+\mu$ is:EasySingle correct
5 Apr 2026, Shift 1 · Q4Consider the system of linear equations in $x, y, z$ : $x + 2y + tz = 0$ , $6x + y + 5tz = 0$ , $3x + t^2y + f(t)\,z = 0$ , where…MediumSingle correct
6 Apr 2026, Shift 2 · Q4The sum of all possible values of $\theta\in[0,2\pi]$ , for which the system of equations : $x\cos 3\theta-8y-12z=0$ …MediumSingle correct
8 Apr 2026, Shift 2 · Q3If the system of linear equations : $x + y + z = 6$ , $x + 2y + 5z = 10$ , $2x + 3y + \lambda z = \mu$ has infinitely many solutions, then…EasySingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.